# Gauss-Seidel method

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## Gauss-Seidel method

[¦gau̇s ′zīd·əl ‚meth·əd]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Some numerical methods such Alternating Group Explicit (AGE) [4], Successive Over Relaxation (SOR), Gauss Seidel (GS), Red Black Gauss Seidel (GSRB) and Jacobi (JB) methods are investigated to select the superior method for solving the curing model.
Table 1: The comparison of numerical results based on some numerical methods Numerical Analysis AGE Gauss Seidel SOR Red-Black Execution time 0.05667s 0.06227s 0.06228s Number of iteration 5 30 30 RMSE 1.77057 4.03773 3.56559 Convergence rate 12 2 2 Numerical Analysis Gauss Seidel Jacobi Execution time 0.06418s 0.06607s Number of iteration 50 60 RMSE 4.93908 5.79083 Convergence rate 1.2 1
Kohno, "Adaptive Gauss Seidel method for linear systems," International Journal of Computer Mathematics, vol.
First, we have to assume initial guess to start the Gauss Seidel Method.
1.5.1 PROGRAM % This function applies N iterations of Gauss Seidel method to the system of non-linear equations Ax = b % x0 is intial value tol =0.01 x0=[0 0 0]; N=100; n = length(x0); x=x0; X=[x0]; for k=1:N %for N iterations %Consider non-linear systems of equations as follows.
One of the best method is Gauss Seidel for solving non-linear systems of equations.
After that we have to choose initial guess to start Gauss Seidel method then substitute the solution in the above equation and use the most recent value.
Advantageously, Gauss Seidel method is very effective concerning computer storage and time requirements.
The results shown by [11] proved that the Successive Over-Relaxation method is faster than the Gauss Seidel and Jacobi methods because of its performance, Number of iterations required to converge and level of accuracy.
Apply Point Gauss Seidel iterations on [u.sub.o] on the finest grid a few times as pre-smoother to get an approximate solution [u.sub.1].
Setup the error equation [L.sub.c][e.sub.c] = [r.sub.c] on the coarser grid and solve for the error e using the Point Gauss Seidel method.

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